A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Consider the figure. Given, AB is equal to the radius of the circle. In △OAB, OA=OB=AB=radius of the circle. Thus, △OAB is an equilateral triangle. and ∠AOC = 60°. Also, ∠ACB = 1/2∠AOB = 1/2 × 60° = 30°. Since, ACBD is a cyclic quadrilateral, ∠ACB + ∠ADB = 180° [Opposite angles of cyclic quadrilateral are supplementary] ⇒ ∠ADB = 180° - 30° = 150°. Thus, the angle subtended by the chord at a point on the minor arc and also at a point on the major arc are 150° and 30°, respectively.